Simplify the following expression: $\sqrt{11}+\sqrt{176}+\sqrt{99}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{11}+\sqrt{176}+\sqrt{99}$ $= \sqrt{11}+\sqrt{16 \cdot 11}+\sqrt{9 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{11}+\sqrt{16} \cdot \sqrt{11}+\sqrt{9} \cdot \sqrt{11}$ $= \sqrt{11}+4\sqrt{11}+3\sqrt{11}$ Finally, simplify by combining the terms. $= ( 1 + 4 + 3 )\sqrt{11} = 8\sqrt{11}$